Improvement on Monte Carlo estimation of HPD intervals
Hoa Le, Uyen Hoang Pham, Nguyễn Thị Kim Phượng, The Bao Pham · Communications in Statistics - Simulation and Computation · 2018
In Bayesian statistics, there have been several methods on estimating the highest probability posterior density (HPD) such as using Monte Carlo approach combined with mean relative error (ME) served as a measure of effectiveness in Chen and Shao (1999 Chen, M. H., and Q. M. Shao. 1999. Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics 8 (1):69–92.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and Chen, Shao and Ibrahim (2012 Chen, M. H., Q. M. Shao, and J. G. Ibrahim. 2012. Monte Carlo methods in Bayesian computation. Berlin: Springer Science & Business Media. [Google Scholar]) for the unimodal case and a simple application to Bayesian hierarchical model. In this paper, we firstly reconsider the former and then propose a new method based on probability density function with an algorithm in order to give an estimation for HPD intervals to improve on Monte Carlo in both unimodal and multimodal cases. We further show that our new method has made an improvement in producing credible intervals with the shortest length for some cases. The necessary theory is developed and illustrative examples are provided.